Logo by S Nelson - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Check out the originating "3d Mandelbulb" thread here
 
*
Welcome, Guest. Please login or register. May 23, 2022, 11:26:23 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: [1]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Split-Complex Numbers?  (Read 2420 times)
0 Members and 1 Guest are viewing this topic.
mjk1093
Forums Freshman
**
Posts: 19



« on: March 10, 2010, 02:53:05 PM »

I was wondering if anyone here knew anything about the Split-Complex numbers, and if you can make interesting fractals with them.

Thanks in advance,
mjk1093
Logged
kram1032
Fractal Senior
******
Posts: 1863


« Reply #1 on: March 10, 2010, 04:14:59 PM »

http://kram1032.deviantart.com/art/dusty-old-attic-128907426 - this is a Buddhabrot with Split Complex numbers wink

Nice but not really interesting.

However, playing with it a bit more can lead to quite interesting results smiley

Dual Numbers result in this Fan-pattern:
http://kram1032.deviantart.com/art/sunset-fans-128739482

And if you cycle through complex, split complex and dual numbers, you get quite interesting patterns like this one:
http://kram1032.deviantart.com/art/battlebrot-128916634
Logged
Timeroot
Fractal Fertilizer
*****
Posts: 362


The pwnge.


WWW
« Reply #2 on: March 11, 2010, 01:02:58 AM »

Neat pics. I'm surprised that the Fan pattern (dual numbers( also produces an interesting image, as the x is independent of the y, and so would always approach either a steady state or infinity... and so y will "almost always" goes to infinity too, if x goes to infinity. If x goes to a steady state, then y will either go to infinity as well (albeit only exponentially fast), or go to a steady state. No, wait... x could be chaotic... never mind.  embarrass

My computer is broken, could someone render a quick escape-time picture of dual numbers? It would be appreciated!  smiley
Logged

Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
kram1032
Fractal Senior
******
Posts: 1863


« Reply #3 on: March 11, 2010, 06:40:57 PM »

I also found it kinda surprising smiley
The split complex (at least for the standard Mset) aren't half as interesting as the dual numbers smiley
Logged
Pages: [1]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
split-complex ternary algebra xD Theory kujonai 7 3724 Last post January 19, 2011, 11:25:14 AM
by jehovajah
the ABSOLIENS: natural generalization of complex numbers at any dimensions ? General Discussion « 1 2 » Yannis 27 4872 Last post January 01, 2013, 05:56:43 PM
by Yannis
Crucifying the Dragon of Complex Numbers Mandelbulb3D Gallery KRAFTWERK 0 501 Last post October 24, 2012, 04:30:04 PM
by KRAFTWERK
Using different inequalities in the rules of complex numbers. Complex Numbers « 1 2 » TheRedshiftRider 21 2192 Last post July 15, 2016, 10:16:44 AM
by jehovajah
Square roots of complex numbers Complex Numbers TheRedshiftRider 0 440 Last post September 26, 2016, 08:33:28 PM
by TheRedshiftRider

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.117 seconds with 24 queries. (Pretty URLs adds 0.01s, 2q)